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AC to DC Rectifier Comparison

@vagplatis
23 hours ago
https://everycircuit.com/circuit/6349910693773312
@Muse - Your circuit compares three stages of AC-to-DC power conversion powered by $9\text{ V}_\text{peak}$, $50\text{ Hz}$ AC sources into identical $40\ \Omega$ resistive loads: ### 1. Half-Wave Rectifier (Top Left) - **Components:** Source #Vs1, single diode #D1, load #R1, measured by #VM1. - **Operation:** Only passes current during the positive half-cycle when the diode is forward-biased. During the negative half-cycle, #D1 blocks current. - **Output:** Output voltage pulses once every $20\text{ ms}$ ($50\text{ Hz}$), reaching a peak of: $$V_\text{peak} \approx 9\text{ V} - 0.7\text{ V} = 8.3\text{ V}$$ The negative half of the cycle is completely lost, resulting in high ripple and low average DC voltage ($V_\text{avg} \approx \frac{V_\text{peak}}{\pi} \approx 2.6\text{ V}$). ### 2. Full-Wave Bridge Rectifier (Top Right) - **Components:** Source #Vs2, diode bridge (#D2a, #D2b, #D2c, #D2d), load #R2, measured by #VM2. - **Operation:** - On the positive half-cycle, current flows through #D2a $\rightarrow$ #R2 $\rightarrow$ #D2d. - On the negative half-cycle, current flows through #D2b $\rightarrow$ #R2 $\rightarrow$ #D2c. - **Output:** Current always flows in the same direction through #R2 on both half-cycles, producing pulses at $100\text{ Hz}$ (twice the line frequency). Peak output is lower by two diode drops: $$V_\text{peak} \approx 9\text{ V} - 2 \times 0.7\text{ V} = 7.6\text{ V}$$ Because conduction occurs every half-cycle, the average DC output doubles compared to half-wave ($V_\text{avg} \approx \frac{2 V_\text{peak}}{\pi} \approx 4.8\text{ V}$). ### 3. Filtered Full-Wave Rectifier (Bottom Left) - **Components:** Source #Vs3, diode bridge (#D3a–#D3d), smoothing capacitor #C1 ($1.7\text{ mF}$), load #R3, measured by #VM3. - **Operation:** Reservoir capacitor #C1 charges quickly to the peak voltage during each peak and discharges slowly through #R3 between peaks. - **Output:** Converts the pulsing DC into a smooth DC voltage with minimal ripple. With an RC time constant of $\tau = 40\ \Omega \times 1.7\text{ mF} = 68\text{ ms}$ (much larger than the $10\text{ ms}$ half-period), the voltage stays near $7\text{–}7.5\text{ V}_\text{DC}$. ### Unconnected Element - #T1 is currently unconnected on the schematic grid. It is configured as a step-down transformer ($230\text{ V} \rightarrow 9\text{ V}$), meant to convert mains voltage to the $9\text{ V}$ level used by your rectifiers.
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